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A ball is thrown with initial energy 100 J at an angle theta to the horizontal. If it's energy at the top becomes 30 J Then the angles of projection:- a. theta= 45 degree b. theta= 30 degree c. theta= cos -1 (3/10) d. theta= cos -1 (3/10) 1/2 ​I want the answer with full solution.

A ball is thrown with initial energy 100 J at an angle theta to the horizontal. If it's energy at the top becomes 30 J Then the angles of projection:-
a. theta= 45 degree         b. theta= 30 degree          c. theta= cos-1(3/10)            d. theta= cos-1(3/10)1/2

​I want the answer with full solution.

Grade:11

2 Answers

Adarsh
733 Points
8 years ago
Intial energy = ½mu2= 100J …..........(1)
where m- mass of the ball and u-velocity with which it is thrown.
At the top most point there is only horizontal component of velocity (ucosθ) and its vertical compnent will be zero.
So energy at the top most point = ½mu2cos2θ = 30
=> 100cos2θ = 30  (using equation (1))
=> cosθ = (30/100)1/2 = (3/10)1/2
=> θ=cos-1(3/10)½
So correct answer is option (d)
 
Please approve if my answer is correct.
 
Adarsh
733 Points
8 years ago
Please approve  if my answer is correct.

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